arXiv subjects

Tung D. Nguyen

Publications and source records attributed to Tung D. Nguyen.

16 recordsLinked to original sources

arXiv2026

Computing with reaction networks at input-independent speed: exponential and logarithmic functions

The concept of \textit{input-independent computational speed} for chemistry-based analog computers was introduced in Anderson-Joshi (2025), where it was shown that arithmetic operations can be computed with a convergence rate bounded below independently of the input values. Here, by inputs we mean the numerical values encoded by the initial concentrations of designated input species, with the underlying reaction network and rate constants held fixed. Combining these operations via power series to approximate transcendental functions is possible in principle, but the number of chemical species required grows with the number of terms retained, and achieving sufficient accuracy may demand many terms---a burden that is especially severe for slowly converging series such as the power series for the logarithm. In this paper, we begin the program of directly computing transcendental functions by chemical reaction networks by focusing on the exponential and logarithmic functions, two widely used transcendental functions, and constructing reaction network modules that compute them without relying on truncated power series. We show that the resulting modules are mass-action systems, and prove that they achieve arbitrary accuracy given sufficient time while operating at input-independent speed. Moreover, these modules can be combined with each other and with the arithmetic modules of Anderson-Joshi (2025): any such composite computation also runs at input-independent speed, with a convergence rate that does not depend on the length of the feedforward chain. Logarithm and exponential functions serve as foundational cases, and the constructions developed here are intended to serve as templates for the direct computation of more general transcendental functions by chemical reaction networks.

math.DS↗

arXiv2026

Bistability, Absolute Concentration Robustness, and Hysteresis in Dual-Site Futile Cycles with Bifunctional Enzymes

Bifunctional enzymes, which catalyze both the forward and reverse steps of a substrate modification reaction, arise naturally in bacterial two-component signaling systems and metabolic regulation. Beyond their well-known role in conferring absolute concentration robustness (ACR) on substrate species, bifunctional enzymes profoundly shape the dynamical landscape of the networks in which they appear. We study a class of dual-site futile cycles in which the reverse modification steps are carried out by bifunctional enzyme-substrate compounds, and provide a complete mathematical analysis of all four such networks, characterizing the existence, number, and stability of steady states, as well as the bifurcation structure as total substrate is varied. All four networks admit boundary steady states, in contrast to the non-bifunctional case. The networks differ in the number and stability of boundary steady states, in the maximum number of positive steady states (ranging from two to four), and in whether bistability is present. In two networks, a transcritical bifurcation connects the boundary and positive steady state branches; in one case this is a backward bifurcation, producing hysteresis. Perhaps the most striking phenomenon occurs in one of the four networks, which simultaneously exhibits bistability and ACR in the final modification state, where the system can settle into either of two stable steady states with different intermediate concentrations yet identical final product concentration.

math.DS↗

arXiv2026

Optimal Harvesting in Stream Networks: Maximizing Biomass and Yield

In this study, we develop a metapopulation model framework to identify optimal harvesting strategies for a population in a stream network. We consider two distinct optimization objectives: maximization of total biomass and maximization of total yield, under the constraint of a fixed total harvesting effort. We examine in detail the special case of a two-patch network and fully characterize the optimal strategies for each objective. We show that when the population growth rate exceeds a critical threshold, a single harvesting strategy can simultaneously maximize both objectives. For general $n$-patch networks with homogeneous growth rates across patches, we focus on the regime of large growth rates and demonstrate that the optimal harvesting strategy selects patches according to their intraspecific competition rates and an effective net flow metric determined by network connectivity parameters.

math.DS↗

arXiv2026

A disease-spread model on hypergraphs with distinct droplet and aerosol transmission modes

We examine the spread of an infectious disease, such as one that is caused by a respiratory virus, with two distinct modes of transmission. To do this, we consider a susceptible--infected--susceptible (SIS) disease on a hypergraph, which allows us to incorporate the effects of both dyadic (i.e., pairwise) and polyadic (i.e., group) interactions on disease propagation. This disease can spread either via large droplets through direct social contacts, which we associate with edges (i.e., hyperedges of size 2), or via infected aerosols in the environment through hyperedges of size at least 3 (i.e., polyadic interactions). We derive mean-field approximations of our model for two types of hypergraphs, and we obtain threshold conditions that characterize whether the disease dies out or becomes endemic. Additionally, we numerically simulate our model and a mean-field approximation of it to examine the impact of various factors, such as hyperedge size (when the size is uniform), hyperedge-size distribution (when the sizes are nonuniform), and hyperedge-recovery rates (when the sizes are nonuniform) on the disease dynamics.

physics.soc-ph↗

arXiv2025

Bifunctional enzyme action as a source of robustness in biochemical reaction networks: a novel hypergraph approach

Substrate modification networks are ubiquitous in living, biochemical systems. A higher-level hypergraph "skeleton" captures key information about which substrates are transformed in the presence of modification-specific enzymes. Many different detailed models can be associated to the same skeleton, however uncertainty related to model fitting increases with the level of detail. We show that essential dynamical properties such as existence of positive steady states and concentration robustness can be extracted directly from the skeleton independent of the detailed model. The novel formalism of directed hypergraphs is used to prove that bifunctional enzyme action plays a key role in generating robustness. Moreover, we use another novel concept of "current" on a directed hypergraph to establish a link between potentially remote network components. Current is an essential notion required for existence of positive steady states, and furthermore, current-matching combined with bifunctionality generates concentration robustness.

q-bio.MN↗

arXiv2025

Impact of network connectivity on the dynamics of populations in stream environments

We consider the impact of network connectivity on the dynamics of a population in a stream environment. The population is modeled using a graph theoretical framework, with habitats represented by isolated patches. We introduce a change in connectivity into the model through the addition of a bi-directional or one-directional edge between two patches and examine the impact of this edge modification on the metapopulation growth rate and the network biomass. Our main results indicate that adding a bi-directional edge often decreases both measures, while the effect of adding an one-directional edge is more intricate and dependent on the model parameters. We establish complete analytical results for stream networks of three patches, and provide some generalizations and conjectures for more general stream networks of $n$ patches. These conjectures are supported with numerical simulations.

q-bio.PE↗

arXiv2024

Bifunctional enzyme provides absolute concentration robustness in multisite covalent modification networks

Biochemical covalent modification networks exhibit a remarkable suite of steady state and dynamical properties such as multistationarity, oscillations, ultrasensitivity and absolute concentration robustness. This paper focuses on conditions required for a network to have a species with absolute concentration robustness. We find that the robustness in a substrate is endowed by its interaction with a bifunctional enzyme, which is an enzyme that has different roles when isolated versus when bound as a substrate-enzyme complex. When isolated, the bifunctional enzyme promotes production of more molecules of the robust species while when bound, the same enzyme facilitates degradation of the robust species. These dual actions produce robustness in the large class of covalent modification networks. For each network of this type, we find the network conditions for the presence of robustness, the species that has robustness, and its robustness value. The unified approach of simultaneously analyzing a large class of networks for a single property, i.e. absolute concentration robustness, reveals the underlying mechanism of the action of bifunctional enzyme while simultaneously providing a precise mathematical description of bifunctionality.

q-bio.MN↗

arXiv2023

Impact of resource distributions on the competition of species in stream environment

Our earlier work in \cite{nguyen2022population} shows that concentrating the resources on the upstream end tends to maximize the total biomass in a metapopulation model for a stream species. In this paper, we continue our research direction by further considering a Lotka-Voletrra competition patch model for two stream species. We show that the species whose resource allocations maximize the total biomass has competitive advantage.

q-bio.PE↗

arXiv2023

Maximizing Metapopulation Growth Rate and Biomass in Stream Networks

We consider the logistic metapopulation model over a stream network and use the metapopulation growth rate and the total biomass (of the positive equilibrium) as metrics for different aspects of population persistence. Our objective is to find distributions of resources that maximize these persistence measures. We begin our study by considering stream networks consisting of three nodes and prove that the strategy to maximize the total biomass is to concentrate all the resources in the most upstream locations. In contrast, when the diffusion rates are sufficiently small, the metapopulation growth rate is maximized when all resources are concentrated in one of the most downstream locations. These two main results are generalized to stream networks with any number of patches.

math.DS↗

arXiv2023

Prevalence of multistationarity and absolute concentration robustness in reaction networks

For reaction networks arising in systems biology, the capacity for two or more steady states, that is, multistationarity, is an important property that underlies biochemical switches. Another property receiving much attention recently is absolute concentration robustness (ACR), which means that some species concentration is the same at all positive steady states. In this work, we investigate the prevalence of each property while paying close attention to when the properties occur together. Specifically, we consider a stochastic block framework for generating random networks, and prove edge-probability thresholds at which - with high probability - multistationarity appears and ACR becomes rare. We also show that the small window in which both properties occur only appears in networks with many species. Taken together, our results confirm that, in random reversible networks, ACR and multistationarity together, or even ACR on its own, is highly atypical. Our proofs rely on two prior results, one pertaining to the prevalence of networks with deficiency zero, and the other "lifting" multistationarity from small networks to larger ones.

math.PR↗

arXiv2022

Deep Learning Generates Synthetic Cancer Histology for Explainability and Education

Artificial intelligence methods including deep neural networks (DNN) can provide rapid molecular classification of tumors from routine histology with accuracy that matches or exceeds human pathologists. Discerning how neural networks make their predictions remains a significant challenge, but explainability tools help provide insights into what models have learned when corresponding histologic features are poorly defined. Here, we present a method for improving explainability of DNN models using synthetic histology generated by a conditional generative adversarial network (cGAN). We show that cGANs generate high-quality synthetic histology images that can be leveraged for explaining DNN models trained to classify molecularly-subtyped tumors, exposing histologic features associated with molecular state. Fine-tuning synthetic histology through class and layer blending illustrates nuanced morphologic differences between tumor subtypes. Finally, we demonstrate the use of synthetic histology for augmenting pathologist-in-training education, showing that these intuitive visualizations can reinforce and improve understanding of histologic manifestations of tumor biology.

eess.IV↗

arXiv2021

Prevalence of deficiency zero reaction networks in an Erdos-Renyi framework

Reaction networks are commonly used within the mathematical biology and mathematical chemistry communities to model the dynamics of interacting species. These models differ from the typical graphs found in random graph theory since their vertices are constructed from elementary building blocks, i.e., the species. In this paper, we consider these networks in an Erd\H os-Rényi framework and, under suitable assumptions, derive a threshold function for the network to have a deficiency of zero, which is a property of great interest in the reaction network community. Specifically, if the number of species is denoted by $n$ and if the edge probability is denote by $p_n$, then we prove that the probability of a random binary network being deficiency zero converges to 1 if $\frac{p_n}{r(n)}\to 0$, as $n \to \infty$, and converges to 0 if $\frac{p_n}{r(n)}\to \infty$, as $n \to \infty$, where $r(n)=\frac{1}{n^3}$.

math.PR↗

arXiv2021

Deficiency zero for random reaction networks under a stochastic block model framework

Deficiency zero is an important network structure and has been the focus of many celebrated results within reaction network theory. In our previous paper \textit{Prevalence of deficiency zero reaction networks in an Erd\H os-Rényi framework}, we provided a framework to quantify the prevalence of deficiency zero among randomly generated reaction networks. Specifically, given a randomly generated binary reaction network with $n$ species, with an edge between two arbitrary vertices occurring independently with probability $p_n$, we established the threshold function $r(n)=\frac{1}{n^3}$ such that the probability of the random network being deficiency zero converges to 1 if $\frac{p_n}{r(n)}\to 0$ and converges to 0 if $\frac{p_n}{r(n)}\to\infty$, as $n \to \infty$. With the base Erd\H os-Rényi framework as a starting point, the current paper provides a significantly more flexible framework by weighting the edge probabilities via control parameters $α_{i,j}$, with $i,j\in \{0,1,2\}$ enumerating the types of possible vertices (zeroth, first, or second order). The control parameters can be chosen to generate random reaction networks with a specific underlying structure, such as "closed" networks with very few inflow and outflow reactions, or "open" networks with abundant inflow and outflow. Under this new framework, for each choice of control parameters $\{α_{i,j}\}$, we establish a threshold function $r(n,\{α_{i,j}\})$ such that the probability of the random network being deficiency zero converges to 1 if $\frac{p_n}{r(n,\{α_{i,j}\})}\to 0$ and converges to 0 if $\frac{p_n}{r(n,\{α_{i,j}\})}\to \infty$.

math.PR↗

arXiv2020

Canonical Tensor Scaling

In this paper we generalize the canonical positive scaling of rows and columns of a matrix to the scaling of selected-rank subtensors of an arbitrary tensor. We expect our results and framework will prove useful for sparse-tensor completion required for generalizations of the recommender system problem beyond a matrix of user-product ratings to multidimensional arrays involving coordinates based both on user attributes (e.g., age, gender, geographical location, etc.) and product/item attributes (e.g., price, size, weight, etc.).

math.NA↗

arXiv2020

Q-Learning with Differential Entropy of Q-Tables

It is well-known that information loss can occur in the classic and simple Q-learning algorithm. Entropy-based policy search methods were introduced to replace Q-learning and to design algorithms that are more robust against information loss. We conjecture that the reduction in performance during prolonged training sessions of Q-learning is caused by a loss of information, which is non-transparent when only examining the cumulative reward without changing the Q-learning algorithm itself. We introduce Differential Entropy of Q-tables (DE-QT) as an external information loss detector to the Q-learning algorithm. The behaviour of DE-QT over training episodes is analyzed to find an appropriate stopping criterion during training. The results reveal that DE-QT can detect the most appropriate stopping point, where a balance between a high success rate and a high efficiency is met for classic Q-Learning algorithm.

cs.LG↗

arXiv2017

Results on stochastic reaction networks with non-mass action kinetics

In 2010, Anderson, Craciun, and Kurtz showed that if a deterministically modeled reaction network is complex balanced, then the associated stochastic model admits a stationary distribution that is a product of Poissons \cite{ACK2010}. That work spurred a number of followup analyses. In 2015, Anderson, Craciun, Gopalkrishnan, and Wiuf considered a particular scaling limit of the stationary distribution detailed in \cite{ACK2010}, and proved it is a well known Lyapunov function \cite{ACGW2015}. In 2016, Cappelletti and Wiuf showed the converse of the main result in \cite{ACK2010}: if a reaction network with stochastic mass action kinetics admits a stationary distribution that is a product of Poissons, then the deterministic model is complex balanced \cite{CW2016}. In 2017, Anderson, Koyama, Cappelletti, and Kurtz showed that the mass action models considered in \cite{ACK2010} are non-explosive (so the stationary distribution characterizes the limiting behavior). In this paper, we generalize each of the three followup results detailed above to the case when the stochastic model has a particular form of non-mass action kinetics.

math.PR↗